Hello and thanks for the question. Here are the criteria for figuring out if you have a 1st edition:

Look for Viking's original Address on the copyright page and separately on the dustjacket. You should see 625 Madison Avenue on both.
Look for the words "First Published in 1982" on the copyright page
Look for the issue price of $16.95 on the dustjacket
The book size should be 9.5h x 6.25w (this is the same size as many 1st ed SK books published in the 80's, just slightly taller then the all the 1st edition dark tower books)
Boards should be blue in color, quarter bound in dark blue/navy

So, without the DJ price you can't be absolutely sure, but also I want to point out that the biggest part of the value of the book is in the DJ. Without it even a 1st edition copy would only be worth a few dollars.